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Keeping tires in their ideal temperature range is important. For some very small and light cars it may be difficult to get tires fully up to temp, I've seen this on cars like the Lotus 7 (~1100lbs). With big tires and a really hard compound, a driver may not be able to get the tires to temp.
We played around a bit with tire sizes on the S2000, and the fastest setup was always the largest we had (slicks the equivalent of 285/325's) on a car weighing well under 2400 pounds. Took 1-2 hard laps to really get 'em sticky though.
As for the Corvette story, I would consider the source carefully. I would wager that in any serious (say Speed World Challenge or faster) endeavor, you're not likely to find anybody campaigning a production-based car running any tire smaller than either the maximum allowed by the rules, or the maximum size they can physically fit to the car.
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